1. Field of Invention
This invention relates generally to methods for measuring the viscosity of fluids, and more specifically, to a method for determining the viscosity of a fluid flowing through a system at any point in the system.
2. Description of Related Art
A capillary viscometer is commonly used because of its inherent features such as simplicity, accuracy, similarity to process flows like extrusion dies, no free surface, etc. Viscous flow in capillary viscometry is firmly established both theoretically and experimentally. C. W. Macosko, Rheology: Principles, Measurements, and Applications (VCH, 1993). In fact, the capillary viscometer was the first viscometer and this device remains the most common for measuring viscosity for polymer solutions and other non-Newtonian fluids. However, most existing capillary viscometers produce viscosity measurement a shear rate at a time. In the case of Newtonian fluids the observation of the rate of flow at a single pressure drop is sufficient to define the flow behavior. However, in the case of non-Newtonian fluids, viscosity measurements need to be performed over a range of shear rates. In order to measure viscosity over a range of shear rates, it is necessary to repeat the measurement by varying either the driving pressure head or the capillary tube diameter, which leads to a time-consuming measurement requiring intensive labor. Hence, these methods are not suited for measuring the rheology of polymer fluids that may exhibit shear-dependent viscosities. Furthermore, application of such techniques often requires relatively large volumes of the test fluids. Therefore, there has been a need to develop a simple and labor-free viscometer which can measure the viscosity of fluids over shear rates at a time.
In U.S. Pat. No. 6,019,735 (Kensey et al.) and U.S. Pat. No. 6,077,234 (Kensey et al.), which are assigned to the same Assignee, namely Rheologics, Inc., of the present invention, there is disclosed a scanning-capillary-tube viscometer for measuring the viscosity of a fluid, e.g., circulating blood of a living being. Among other things, this scanning capillary tube viscometer discloses an apparatus that monitors the changing height of a column of fluid versus time in a riser that is in fluid communication with a living being""s circulating blood. A further improvement of this type of scanning capillary tube viscometer is disclosed in U.S. Pat. No. 6,322,524 (Kensey et al.) and U.S. Pat. No. 6,402,703 (Kensey et al.), both entitled DUAL RISER/SINGLE CAPILLARY VISCOMETER, which are assigned to the same Assignee as the present invention, namely, Rheologics, Inc. and whose entire disclosures are incorporated by reference herein. In those patents, a U-shaped tube structure is utilized that generates a falling and rising column of test fluid that is driven by a decreasing pressure differential for moving these columns of fluid through a plurality of shear rates, which is necessary for non-Newtonian fluid (e.g., blood) viscosity determinations. Such an apparatus can produce viscosity data in a low shear range (e.g., approximately 0.2 sxe2x88x921).
However, there remains a need, especially in the field of blood rheology, for determining a unique viscosity-shear rate relationship for a particular fluid in a system that describes the fluid viscosity over a wide range of shear rates. For example, it would be extremely desirable to have a unique viscosity-shear rate relationship for the circulating blood of an individual. By determining such a unique relationship, a physician could accurately determine the viscosity at any particular location in the individual""s circulatory system by simply measuring the shear rate of the circulating blood at that location and then plugging that shear rate into that individual""s unique viscosity-shear rate relationship. Moreover, by taking a plurality of shear rate measurements throughout the individual""s circulatory system, determining the respective viscosities and then multiplying these viscosities by the respective shear rates, a physician can also develop a shear stress profile for that individual""s circulatory system.
A method for determining the viscosity of a fluid flowing through a system at any point in the system. The method comprises the steps of: (a) determining a characteristic relationship for the fluid between viscosity and shear rate; (b) obtaining a shear rate of the fluid as it moves through at least one position in the system; and (c) determining the viscosity of the fluid at the at least one position by applying the shear rate to the characteristic relationship.